Technical Report Extended Figures

Document Introduction

This will instead include a document summary section, a project summary, and links to other important documentation.

Model code example

Show the code
## RTMB dat and par setup ####
# Dat
dat <- list(srdat = srdat,
            WAbase = WAbase,
            WAin = WAin,
            lineWA =  seq(min(WAbase$logWAshifted), 
                          max(WAbase$logWAshifted), 0.1), # Not added to NLL
            mean_logWA = mean_logWA,
            logRS = log(srdat$Rec) - log(srdat$Sp),
            prioronly = 0) # 0-run with data, 1-prior prediction mode

# External vectors
N_Stk <- max(srdat$Stocknumber + 1)
N_Obs <- nrow(srdat)
stk = srdat$Stocknumber + 1
lhdiston <- T 
bias.cor <- F 

# Parameters/Initial values
par <- list(b0 = c(10, 0), # Initial values for WA regression intercepts
            bWA = c(0, 0), # Inital values for WA regression slopes
            logSREP_re = numeric(N_Stk), # Zeroes
            logAlpha0 = 0.6,
            logAlpha_re = numeric(nrow(dat$WAbase)), # Zeroes
            tauobs = 0.01 + numeric(N_Stk), # Constrained positive
            logSREP_sd = 1, 
            logAlpha_sd = 1
)
if (lhdiston) {
  par$logAlpha02 <- 0
}

f_srep <- function(par){
  getAll(dat, par)
  
  N_Stk = max(srdat$Stocknumber + 1) # number of stocks
  stk = srdat$Stocknumber + 1 # vector of stocknumbers
  N_Obs = nrow(srdat) # number of observations
  N_Pred = nrow(WAin) # number of predicted watershed areas
  
  S = srdat$Sp
  type = lifehist$lh
  type_tar = as.numeric(WAin$lh) 

  SREP <- numeric(N_Stk)
  # logE_pred <- numeric(N_Stk)
  logSREP <- numeric(N_Stk)
  logAlpha <- numeric(N_Stk)
  
  logRS_pred <- numeric(N_Obs) 

  SREP_tar <- numeric(N_Pred)
  logSREP_tar <- numeric(N_Pred)
  logAlpha_tar <- numeric(N_Pred)
  
  # Simulated line vectors
  line <- length(lineWA)
  logSREP_line_stream <- numeric(line)
  SREP_line_stream <- numeric(line)
  logSREP_line_ocean <- numeric(line)
  SREP_line_ocean <- numeric(line)
  
  if (bias.cor) {
    biaslogSREP <- -0.5*logSREP_sd^2
    biaslogAlpha <- -0.5*logAlpha_sd^2
    biaslogRS <- -0.5*(sqrt(1/tauobs))^2
  } else {
    biaslogSREP <- 0
    biaslogAlpha <- 0
    biaslogRS <- numeric(N_Stk)
  }
  
  nll <- 0 # Begin negative log-likelihood
  
  nll <- nll - sum(dnorm(b0[1], 10, sd = 31.6, log = TRUE)) # Prior
  nll <- nll - sum(dnorm(b0[2], 0, sd = 31.6, log = TRUE)) # Prior
  nll <- nll - sum(dnorm(bWA[1], 0, sd = 31.6, log = TRUE)) # Prior
  nll <- nll - sum(dnorm(bWA[2], 0, sd = 31.6, log = TRUE)) # Prior
  
  nll <- nll - sum(dnorm(logAlpha0, 0.6, sd = 0.45, log = TRUE)) # Prior (rM)
  if(lhdiston) nll <- nll - sum(dnorm(logAlpha02, 0, sd = 31.6, log = TRUE)) # Prior (rD)
  
  ## Second level of hierarchy - Ricker parameters:
  for (i in 1:N_Stk){
    nll <- nll - dnorm(logSREP_re[i], 0, sd = 1, log = TRUE) 
    
    logSREP[i] <- b0[1] + b0[2]*type[i] + (bWA[1] + bWA[2]*type[i]) * WAbase$logWAshifted[i] + logSREP_re[i]*logSREP_sd + biaslogSREP
    SREP[i] <- exp(logSREP[i])
    
    nll <- nll - dnorm(logAlpha_re[i], 0, sd = 1, log = TRUE) 

    if(lhdiston) logAlpha[i] <- logAlpha0 + logAlpha02*type[i] + logAlpha_re[i]*logAlpha_sd + biaslogAlpha
    else logAlpha[i] <- logAlpha0 + logAlpha_re[i]*logAlpha_sd + biaslogAlpha

    nll <- nll - dgamma(tauobs[i], shape = 0.0001, scale = 1/0.0001, log = TRUE)
  }

  ## First level of hierarchy: Ricker model:
  for (i in 1:N_Obs){
    logRS_pred[i] <- logAlpha[stk[i]]*(1 - S[i]/SREP[stk[i]]) + biaslogRS[stk[i]]

    if(!prioronly){
      nll <- nll - dnorm(logRS[i], logRS_pred[i], sd = sqrt(1/tauobs[stk[i]]), log = TRUE)
    } 
      
  }
  
  ## Calculate SMSY for Synoptic set - for plotting
  SMSY_r = numeric(nrow(WAbase))
  BETA_r = numeric(nrow(WAbase))
  
  for (i in 1:N_Stk){
    BETA_r[i] <- logAlpha[i] / SREP[i]
    SMSY_r[i] <- (1 - LambertW0(exp(1 - logAlpha[i]))) / BETA_r[i]
  }

  ## PREDICTIONS
  BETA = numeric(nrow(WAin))
  SMSY = numeric(nrow(WAin))
  SGEN = numeric(nrow(WAin))

  for (i in 1:N_Pred){
    if(lhdiston) logAlpha_tar[i] <- logAlpha0 + logAlpha02*type_tar[i] + biaslogAlpha 
    else logAlpha_tar[i] <- logAlpha0 + biaslogAlpha

    logSREP_tar[i] <- b0[1] + b0[2]*type_tar[i] + (bWA[1] + bWA[2]*type_tar[i])*WAin$logWAshifted_t[i] + biaslogSREP
    SREP_tar[i] <- exp(logSREP_tar[i])
    
    # Predict BETA
    BETA[i] <- logAlpha_tar[i]/SREP_tar[i]
    # Predict SMSY
    SMSY[i] <- (1-LambertW0(exp(1-logAlpha_tar[i])))/BETA[i]
    # Predict SGEN
    SGEN[i] <- -1/BETA[i]*LambertW0(-BETA[i]*SMSY[i]/(exp(logAlpha_tar[i])))
  }
  
  # Create predictions on an simulated line
  for (i in 1:line){
    logSREP_line_ocean[i] <- b0[1] + b0[2] + (bWA[1] + bWA[2])*lineWA[i] + biaslogSREP # DATA - not in likelihood
    SREP_line_ocean[i] <- exp(logSREP_line_ocean[i])
    
    logSREP_line_stream[i] <- b0[1] + (bWA[1])*lineWA[i] + biaslogSREP # DATA - not in likelihood
    SREP_line_stream[i] <- exp(logSREP_line_stream[i])
  }
  
  ## ADREPORT - internal values (synoptic specific/Ricker)  
  REPORT(b0) # Testing simulate()
  REPORT(bWA) # Testing simulate()

  REPORT(logRS_pred)
  
  alpha <- exp(logAlpha)
  # REPORT(logRS) # logRS for all 501 data points
  REPORT(logSREP_re)
  REPORT(logSREP_sd)
  REPORT(SREP) # E (Srep) for all synoptic data set rivers (25)
  REPORT(logSREP)
  REPORT(logAlpha) # model logAlpha (25)
  REPORT(logAlpha0)
  REPORT(logAlpha02)
  REPORT(logAlpha_re) # random effect parameter for resampling
  REPORT(logAlpha_sd)
  REPORT(alpha)
  REPORT(SMSY_r)
  REPORT(BETA_r)
  REPORT(tauobs) # Necessary to add back in observation error?

  alpha_tar <- exp(logAlpha_tar)
  
  REPORT(SREP_tar)
  REPORT(logSREP_tar)
  REPORT(logAlpha_tar)
  REPORT(alpha_tar)
  
  REPORT(BETA)
  REPORT(SMSY)
  REPORT(SGEN)
  
  # Simulated line values for plotting
  REPORT(SREP_line_stream) 
  REPORT(logSREP_line_stream) 
  REPORT(SREP_line_ocean) 
  REPORT(logSREP_line_ocean)
  
  nll # output of negative log-likelihood
}

Extended Results Section: Figures and Tables

1. Model Parameter Trace Plots

b0

b0[1]



b0[2]



bWA

bWA[1]



bWA[2]



logAlpha_re

logAlpha_re[1]



logAlpha_re[2]



logAlpha_re[3]



logAlpha_re[4]



logAlpha_re[5]



logAlpha_re[6]



logAlpha_re[7]



logAlpha_re[8]



logAlpha_re[9]



logAlpha_re[10]



logAlpha_re[11]



logAlpha_re[12]



logAlpha_re[13]



logAlpha_re[14]



logAlpha_re[15]



logAlpha_re[16]



logAlpha_re[17]



logAlpha_re[18]



logAlpha_re[19]



logAlpha_re[20]



logAlpha_re[21]



logAlpha_re[22]



logAlpha_re[23]



logAlpha_re[24]



logAlpha_re[25]



logAlpha_sd

logAlpha_sd



logAlpha0

logAlpha0



logAlpha02

logAlpha02



logSREP_re

logSREP_re[1]



logSREP_re[2]



logSREP_re[3]



logSREP_re[4]



logSREP_re[5]



logSREP_re[6]



logSREP_re[7]



logSREP_re[8]



logSREP_re[9]



logSREP_re[10]



logSREP_re[11]



logSREP_re[12]



logSREP_re[13]



logSREP_re[14]



logSREP_re[15]



logSREP_re[16]



logSREP_re[17]



logSREP_re[18]



logSREP_re[19]



logSREP_re[20]



logSREP_re[21]



logSREP_re[22]



logSREP_re[23]



logSREP_re[24]



logSREP_re[25]



logSREP_sd

logSREP_sd



lp__

lp__



tauobs

tauobs[1]



tauobs[2]



tauobs[3]



tauobs[4]



tauobs[5]



tauobs[6]



tauobs[7]



tauobs[8]



tauobs[9]



tauobs[10]



tauobs[11]



tauobs[12]



tauobs[13]



tauobs[14]



tauobs[15]



tauobs[16]



tauobs[17]



tauobs[18]



tauobs[19]



tauobs[20]



tauobs[21]



tauobs[22]



tauobs[23]



tauobs[24]



tauobs[25]



2. Model Parameter Autocorrelation Plots

b0

b0[1]



b0[2]



bWA

bWA[1]



bWA[2]



logAlpha_re

logAlpha_re[1]



logAlpha_re[2]



logAlpha_re[3]



logAlpha_re[4]



logAlpha_re[5]



logAlpha_re[6]



logAlpha_re[7]



logAlpha_re[8]



logAlpha_re[9]



logAlpha_re[10]



logAlpha_re[11]



logAlpha_re[12]



logAlpha_re[13]



logAlpha_re[14]



logAlpha_re[15]



logAlpha_re[16]



logAlpha_re[17]



logAlpha_re[18]



logAlpha_re[19]



logAlpha_re[20]



logAlpha_re[21]



logAlpha_re[22]



logAlpha_re[23]



logAlpha_re[24]



logAlpha_re[25]



logAlpha_sd

logAlpha_sd



logAlpha0

logAlpha0



logAlpha02

logAlpha02



logSREP_re

logSREP_re[1]



logSREP_re[2]



logSREP_re[3]



logSREP_re[4]



logSREP_re[5]



logSREP_re[6]



logSREP_re[7]



logSREP_re[8]



logSREP_re[9]



logSREP_re[10]



logSREP_re[11]



logSREP_re[12]



logSREP_re[13]



logSREP_re[14]



logSREP_re[15]



logSREP_re[16]



logSREP_re[17]



logSREP_re[18]



logSREP_re[19]



logSREP_re[20]



logSREP_re[21]



logSREP_re[22]



logSREP_re[23]



logSREP_re[24]



logSREP_re[25]



logSREP_sd

logSREP_sd



lp__

lp__



tauobs

tauobs[1]



tauobs[2]



tauobs[3]



tauobs[4]



tauobs[5]



tauobs[6]



tauobs[7]



tauobs[8]



tauobs[9]



tauobs[10]



tauobs[11]



tauobs[12]



tauobs[13]



tauobs[14]



tauobs[15]



tauobs[16]



tauobs[17]



tauobs[18]



tauobs[19]



tauobs[20]



tauobs[21]



tauobs[22]



tauobs[23]



tauobs[24]



tauobs[25]



3. Model Parameter Pairs Plots

Show figure: Pairs Plots

4. Convergence Diagnostic Statistics Table

Geweke Statistics

Show table
Parameter Chain1 Chain2 Chain3 Chain4
b0[1] -1.478 0.678 0.526 -0.176
b0[2] 2.562 -0.712 -0.572 -0.429
bWA[1] -0.801 -2.093 -0.692 0.380
bWA[2] 0.839 -0.174 0.621 -0.302
logSREP_re[1] -0.818 1.114 0.657 0.573
logSREP_re[2] 1.066 0.488 0.653 0.050
logSREP_re[3] 1.860 -0.048 1.489 -0.338
logSREP_re[4] 0.767 -1.123 1.806 0.629
logSREP_re[5] 0.306 -0.671 -0.744 -0.018
logSREP_re[6] 0.982 -1.024 -0.916 0.026
logSREP_re[7] 0.417 -1.477 -1.103 0.610
logSREP_re[8] -0.196 -0.085 -1.257 0.724
logSREP_re[9] 0.388 -1.350 -0.286 0.573
logSREP_re[10] -1.321 1.816 0.654 1.200
logSREP_re[11] -0.518 -0.574 0.020 0.816
logSREP_re[12] -0.617 -1.143 0.052 -0.014
logSREP_re[13] -1.825 0.620 -0.257 0.693
logSREP_re[14] -0.787 0.104 0.793 0.414
logSREP_re[15] 0.897 -1.892 -0.564 0.376
logSREP_re[16] 2.517 -0.231 -0.177 0.510
logSREP_re[17] 1.308 0.643 0.496 -0.651
logSREP_re[18] 1.948 -0.457 0.574 0.874
logSREP_re[19] 0.772 0.291 1.259 -0.053
logSREP_re[20] -1.245 1.202 -1.241 -0.873
logSREP_re[21] -0.043 -0.605 -0.307 1.297
logSREP_re[22] -1.431 1.576 1.504 1.099
logSREP_re[23] 0.455 0.880 -0.183 -0.187
logSREP_re[24] -1.952 -0.265 -1.027 -0.456
logSREP_re[25] -1.964 0.488 1.715 0.954
logAlpha0 -0.735 -1.040 -1.453 -0.998
logAlpha_re[1] 0.496 -1.772 0.447 -0.896
logAlpha_re[2] -1.449 -1.607 -0.566 0.416
logAlpha_re[3] -0.659 -0.046 2.075 0.385
logAlpha_re[4] 1.020 0.848 -1.472 -0.252
logAlpha_re[5] 2.105 1.101 3.849 1.352
logAlpha_re[6] 0.097 -0.491 1.364 0.508
logAlpha_re[7] -0.099 -0.371 0.169 -0.169
logAlpha_re[8] 0.017 -1.036 1.216 -0.406
logAlpha_re[9] 2.250 1.114 1.575 -0.903
logAlpha_re[10] 1.263 -1.551 -1.220 0.704
logAlpha_re[11] 2.610 0.993 -0.120 -0.493
logAlpha_re[12] 0.767 0.492 -0.501 0.573
logAlpha_re[13] 0.125 0.646 0.694 0.712
logAlpha_re[14] 0.210 0.193 0.291 0.395
logAlpha_re[15] 0.577 1.760 0.516 1.587
logAlpha_re[16] 0.077 -0.221 -1.000 -1.796
logAlpha_re[17] 2.545 1.574 1.468 0.702
logAlpha_re[18] 0.738 0.426 -0.741 -0.436
logAlpha_re[19] 1.292 0.116 1.032 0.058
logAlpha_re[20] -0.365 -1.227 0.265 0.080
logAlpha_re[21] 0.688 1.061 0.501 -0.636
logAlpha_re[22] 0.566 -0.771 -1.244 0.331
logAlpha_re[23] -0.168 0.017 0.738 0.945
logAlpha_re[24] 0.037 -0.013 -0.829 0.204
logAlpha_re[25] 0.616 0.099 0.670 -0.337
tauobs[1] -0.205 1.222 0.010 -0.569
tauobs[2] 1.568 -0.863 0.456 -0.876
tauobs[3] -1.845 0.568 0.004 0.629
tauobs[4] 0.277 1.259 -1.279 0.874
tauobs[5] 1.070 0.863 -0.809 -0.430
tauobs[6] -0.735 -0.466 0.022 0.426
tauobs[7] -2.194 1.267 2.178 -0.725
tauobs[8] -0.242 -1.496 -0.593 -0.645
tauobs[9] 1.533 0.561 -0.382 -0.983
tauobs[10] 0.795 -1.397 1.576 0.233
tauobs[11] -1.035 1.485 -1.533 -1.563
tauobs[12] 0.074 0.298 -2.962 0.983
tauobs[13] -1.569 -0.592 -0.015 0.651
tauobs[14] -1.562 0.584 0.871 1.600
tauobs[15] 1.728 1.924 0.091 0.785
tauobs[16] -0.599 0.741 -0.900 0.641
tauobs[17] 1.460 0.869 0.859 -0.110
tauobs[18] -0.290 -0.411 -0.026 -1.581
tauobs[19] 1.236 -0.732 1.602 -1.161
tauobs[20] 1.167 1.049 0.405 0.951
tauobs[21] -1.089 0.784 0.415 0.632
tauobs[22] 0.958 -1.053 -1.097 -0.504
tauobs[23] -0.362 -0.951 -0.283 -0.944
tauobs[24] -0.168 1.219 0.455 -1.063
tauobs[25] 0.054 1.521 -0.086 -1.065
logSREP_sd -0.910 -0.970 0.165 -0.171
logAlpha_sd 1.016 2.006 1.245 0.624
logAlpha02 -0.493 0.573 1.011 0.186
lp__ -0.928 1.020 0.149 0.491
Show Chain 1
Show Chain 2
Show Chain 3
Show Chain 4

Heidelberg etc. Statistics

Show Chain 1
stest start pvalue htest mean halfwidth
b0[1] 1 1 0.256 1 8.941 0.010
b0[2] 1 251 0.458 1 1.042 0.015
bWA[1] 1 1 0.394 1 0.680 0.004
bWA[2] 1 1 0.442 1 0.281 0.010
logSREP_re[1] 1 1 0.363 1 0.758 0.043
logSREP_re[2] 1 1 0.448 0 -0.037 0.032
logSREP_re[3] 1 1 0.142 1 1.096 0.033
logSREP_re[4] 1 1 0.917 1 -0.970 0.032
logSREP_re[5] 1 1 0.448 1 -0.740 0.030
logSREP_re[6] 1 1 0.331 1 0.404 0.035
logSREP_re[7] 1 1 0.391 0 0.162 0.035
logSREP_re[8] 1 1 0.335 1 -1.076 0.044
logSREP_re[9] 1 1 0.426 1 0.724 0.037
logSREP_re[10] 1 1 0.419 1 0.433 0.028
logSREP_re[11] 1 1 0.745 0 -0.372 0.042
logSREP_re[12] 1 1 0.834 1 0.756 0.030
logSREP_re[13] 1 1 0.326 1 -0.471 0.025
logSREP_re[14] 1 1 0.769 1 0.913 0.028
logSREP_re[15] 1 1 0.306 0 0.295 0.032
logSREP_re[16] 1 1 0.346 1 1.599 0.030
logSREP_re[17] 1 1 0.375 0 0.048 0.045
logSREP_re[18] 1 251 0.287 1 -0.756 0.033
logSREP_re[19] 1 1 0.715 1 -0.536 0.032
logSREP_re[20] 1 1 0.125 1 -0.862 0.039
logSREP_re[21] 1 1 0.386 1 0.809 0.032
logSREP_re[22] 1 1 0.505 1 -1.269 0.029
logSREP_re[23] 1 1 0.992 0 0.350 0.036
logSREP_re[24] 1 1 0.402 1 -0.364 0.030
logSREP_re[25] 1 1 0.758 1 -0.536 0.028
logAlpha0 1 1 0.521 1 1.560 0.006
logAlpha_re[1] 1 1 0.824 0 -0.337 0.036
logAlpha_re[2] 1 1 0.617 1 -0.762 0.036
logAlpha_re[3] 0 NA 0.005 NA NA NA
logAlpha_re[4] 1 1 0.487 1 -0.359 0.035
logAlpha_re[5] 1 1 0.213 0 0.301 0.032
logAlpha_re[6] 1 1 1.000 1 -0.474 0.034
logAlpha_re[7] 1 1 0.723 0 -0.267 0.031
logAlpha_re[8] 1 1 0.851 0 -0.049 0.042
logAlpha_re[9] 1 1 0.485 1 0.907 0.038
logAlpha_re[10] 1 1 0.507 1 -0.636 0.034
logAlpha_re[11] 1 1 0.054 1 0.435 0.041
logAlpha_re[12] 1 1 0.512 1 0.532 0.030
logAlpha_re[13] 1 1 0.300 0 -0.038 0.031
logAlpha_re[14] 1 1 0.782 1 0.446 0.033
logAlpha_re[15] 1 1 0.292 0 0.361 0.036
logAlpha_re[16] 1 1 0.479 0 -0.052 0.032
logAlpha_re[17] 1 251 0.096 1 0.935 0.035
logAlpha_re[18] 1 1 0.357 1 0.518 0.042
logAlpha_re[19] 1 1 0.116 0 0.192 0.039
logAlpha_re[20] 1 1 0.262 0 -0.286 0.036
logAlpha_re[21] 1 1 0.144 1 0.794 0.034
logAlpha_re[22] 1 1 0.616 1 -0.627 0.037
logAlpha_re[23] 1 1 0.926 0 -0.144 0.034
logAlpha_re[24] 1 1 0.937 0 -0.052 0.037
logAlpha_re[25] 1 1 0.754 0 -0.036 0.032
tauobs[1] 1 1 0.971 1 0.996 0.012
tauobs[2] 1 501 0.061 1 3.306 0.043
tauobs[3] 1 1 0.286 1 3.325 0.039
tauobs[4] 1 1 0.994 1 4.309 0.043
tauobs[5] 1 1 0.230 1 2.543 0.028
tauobs[6] 1 1 0.139 1 4.054 0.044
tauobs[7] 1 1 0.124 1 1.742 0.019
tauobs[8] 1 1 0.333 1 3.124 0.042
tauobs[9] 1 1 0.262 1 4.165 0.049
tauobs[10] 1 1 0.783 1 2.367 0.023
tauobs[11] 1 1 0.424 1 1.811 0.025
tauobs[12] 1 1 0.567 1 5.315 0.054
tauobs[13] 1 1001 0.145 1 5.474 0.073
tauobs[14] 1 1 0.864 1 2.661 0.026
tauobs[15] 1 1 0.745 1 6.427 0.083
tauobs[16] 0 NA 0.006 NA NA NA
tauobs[17] 1 1 0.278 1 6.817 0.072
tauobs[18] 1 1 0.978 1 2.223 0.051
tauobs[19] 1 1 0.115 1 1.769 0.030
tauobs[20] 1 1 0.711 1 2.131 0.026
tauobs[21] 1 1 0.543 1 2.761 0.035
tauobs[22] 1 1 0.362 1 3.072 0.040
tauobs[23] 1 1 0.206 1 2.047 0.020
tauobs[24] 1 1 0.990 1 1.392 0.021
tauobs[25] 1 1 0.772 1 1.469 0.023
logSREP_sd 1 1 0.381 1 0.417 0.006
logAlpha_sd 1 1 0.305 1 0.204 0.007
logAlpha02 1 1 0.697 1 0.292 0.009
lp__ 1 1 0.253 1 -774.481 0.640
Show Chain 2
stest start pvalue htest mean halfwidth
b0[1] 1 1 0.342 1 8.946 0.010
b0[2] 1 1 0.509 1 1.048 0.015
bWA[1] 1 1 0.324 1 0.682 0.004
bWA[2] 1 1 0.960 1 0.281 0.009
logSREP_re[1] 1 1 0.463 1 0.756 0.038
logSREP_re[2] 1 1 0.490 0 -0.066 0.030
logSREP_re[3] 1 1 0.915 1 1.087 0.030
logSREP_re[4] 1 1 0.233 1 -0.992 0.026
logSREP_re[5] 1 1 0.424 1 -0.770 0.026
logSREP_re[6] 1 1 0.526 1 0.400 0.032
logSREP_re[7] 1 1 0.163 0 0.168 0.032
logSREP_re[8] 1 1 0.493 1 -1.072 0.034
logSREP_re[9] 1 1 0.122 1 0.744 0.031
logSREP_re[10] 1 1 0.527 1 0.410 0.025
logSREP_re[11] 1 1 0.733 1 -0.359 0.036
logSREP_re[12] 1 1 0.158 1 0.744 0.032
logSREP_re[13] 1 1 0.951 1 -0.480 0.025
logSREP_re[14] 1 1 0.250 1 0.915 0.029
logSREP_re[15] 1 1 0.096 0 0.286 0.030
logSREP_re[16] 1 1 0.213 1 1.603 0.029
logSREP_re[17] 1 1 0.808 0 0.024 0.039
logSREP_re[18] 1 1 0.700 1 -0.731 0.027
logSREP_re[19] 1 1 0.980 1 -0.558 0.028
logSREP_re[20] 1 1 0.317 1 -0.842 0.033
logSREP_re[21] 1 1 0.249 1 0.774 0.031
logSREP_re[22] 1 1 0.627 1 -1.275 0.028
logSREP_re[23] 1 1 0.902 1 0.357 0.027
logSREP_re[24] 1 1 0.884 1 -0.388 0.027
logSREP_re[25] 1 1 0.644 1 -0.558 0.024
logAlpha0 1 1 0.343 1 1.559 0.006
logAlpha_re[1] 1 1 0.320 1 -0.335 0.026
logAlpha_re[2] 1 1001 0.061 1 -0.698 0.041
logAlpha_re[3] 1 1 0.980 0 -0.199 0.026
logAlpha_re[4] 1 1 0.975 1 -0.387 0.027
logAlpha_re[5] 1 1 0.941 0 0.279 0.028
logAlpha_re[6] 1 1 0.783 1 -0.491 0.026
logAlpha_re[7] 1 1 0.765 0 -0.234 0.027
logAlpha_re[8] 1 1 0.410 0 -0.064 0.035
logAlpha_re[9] 1 501 0.236 1 0.892 0.035
logAlpha_re[10] 1 1 0.083 1 -0.619 0.027
logAlpha_re[11] 1 1 0.300 1 0.407 0.029
logAlpha_re[12] 1 501 0.161 1 0.536 0.032
logAlpha_re[13] 1 1 0.236 0 -0.046 0.025
logAlpha_re[14] 1 1 0.161 1 0.452 0.027
logAlpha_re[15] 1 1 0.181 1 0.340 0.028
logAlpha_re[16] 1 1 0.128 0 -0.094 0.029
logAlpha_re[17] 1 1 0.394 1 0.928 0.030
logAlpha_re[18] 1 1 0.208 1 0.450 0.031
logAlpha_re[19] 1 1 0.129 0 0.220 0.031
logAlpha_re[20] 1 1 0.879 1 -0.344 0.030
logAlpha_re[21] 1 501 0.054 1 0.804 0.037
logAlpha_re[22] 1 1 0.244 1 -0.699 0.034
logAlpha_re[23] 1 1 0.955 0 -0.166 0.025
logAlpha_re[24] 1 1 0.231 0 -0.056 0.026
logAlpha_re[25] 1 1 0.501 0 -0.011 0.027
tauobs[1] 1 1 0.496 1 0.994 0.010
tauobs[2] 1 1 0.783 1 3.343 0.032
tauobs[3] 1 1 0.528 1 3.306 0.030
tauobs[4] 1 1 0.064 1 4.311 0.042
tauobs[5] 1 1 0.598 1 2.533 0.025
tauobs[6] 1 1 0.921 1 4.054 0.035
tauobs[7] 1 1 0.241 1 1.730 0.015
tauobs[8] 1 1 0.454 1 3.082 0.034
tauobs[9] 1 1 0.097 1 4.191 0.041
tauobs[10] 1 251 0.071 1 2.381 0.019
tauobs[11] 1 1 0.247 1 1.795 0.021
tauobs[12] 1 1 0.381 1 5.367 0.045
tauobs[13] 1 1 0.771 1 5.352 0.046
tauobs[14] 1 1 0.290 1 2.637 0.022
tauobs[15] 1 751 0.056 1 6.385 0.074
tauobs[16] 1 1 0.685 1 4.584 0.053
tauobs[17] 1 1 0.135 1 6.774 0.060
tauobs[18] 1 1 0.817 1 2.191 0.044
tauobs[19] 1 1 0.827 1 1.768 0.026
tauobs[20] 1 1 0.401 1 2.135 0.023
tauobs[21] 1 1 0.491 1 2.779 0.028
tauobs[22] 1 1 0.289 1 3.090 0.034
tauobs[23] 1 1 0.713 1 2.042 0.014
tauobs[24] 1 1 0.071 1 1.371 0.016
tauobs[25] 1 1 0.472 1 1.479 0.020
logSREP_sd 1 1 0.209 1 0.410 0.006
logAlpha_sd 1 1 0.118 1 0.209 0.008
logAlpha02 1 1 0.642 1 0.291 0.009
lp__ 1 1 0.080 1 -774.390 0.691
Show Chain 3
stest start pvalue htest mean halfwidth
b0[1] 1 1 0.612 1 8.948 0.011
b0[2] 1 1 0.601 1 1.051 0.015
bWA[1] 1 1 0.453 1 0.683 0.004
bWA[2] 1 1 0.579 1 0.277 0.009
logSREP_re[1] 1 1 0.566 1 0.753 0.033
logSREP_re[2] 1 1 0.641 0 -0.071 0.030
logSREP_re[3] 1 1 0.357 1 1.074 0.031
logSREP_re[4] 1 1 0.868 1 -1.003 0.030
logSREP_re[5] 1 1 0.345 1 -0.768 0.030
logSREP_re[6] 1 1 0.180 1 0.404 0.030
logSREP_re[7] 1 1 0.158 0 0.166 0.032
logSREP_re[8] 1 1 0.140 1 -1.071 0.034
logSREP_re[9] 1 1 0.581 1 0.734 0.034
logSREP_re[10] 1 1 0.277 1 0.414 0.023
logSREP_re[11] 1 1 0.820 1 -0.367 0.036
logSREP_re[12] 1 1 0.662 1 0.737 0.026
logSREP_re[13] 1 1 0.724 1 -0.501 0.021
logSREP_re[14] 1 1 0.191 1 0.899 0.024
logSREP_re[15] 1 1 0.572 0 0.301 0.031
logSREP_re[16] 1 1 0.143 1 1.595 0.028
logSREP_re[17] 1 1 0.736 0 0.011 0.043
logSREP_re[18] 1 1 0.540 1 -0.743 0.030
logSREP_re[19] 1 1 0.415 1 -0.533 0.029
logSREP_re[20] 1 1 0.542 1 -0.838 0.032
logSREP_re[21] 1 1 0.788 1 0.778 0.026
logSREP_re[22] 1 1 0.278 1 -1.291 0.021
logSREP_re[23] 1 1 0.599 1 0.336 0.024
logSREP_re[24] 1 1 0.378 1 -0.391 0.025
logSREP_re[25] 1 1 0.282 1 -0.549 0.025
logAlpha0 1 1 0.362 1 1.557 0.006
logAlpha_re[1] 1 1 0.104 1 -0.331 0.028
logAlpha_re[2] 1 1 0.229 1 -0.735 0.032
logAlpha_re[3] 1 1 0.468 0 -0.189 0.026
logAlpha_re[4] 1 1 0.273 1 -0.364 0.027
logAlpha_re[5] 1 1 0.082 1 0.280 0.027
logAlpha_re[6] 1 1 0.700 1 -0.491 0.027
logAlpha_re[7] 1 1 0.295 0 -0.213 0.025
logAlpha_re[8] 1 1 0.679 0 -0.047 0.033
logAlpha_re[9] 1 1 0.153 1 0.905 0.033
logAlpha_re[10] 1 1 0.580 1 -0.621 0.026
logAlpha_re[11] 1 1 0.502 1 0.385 0.029
logAlpha_re[12] 1 1 0.793 1 0.566 0.028
logAlpha_re[13] 1 1 0.843 0 -0.031 0.025
logAlpha_re[14] 1 1 0.659 1 0.473 0.025
logAlpha_re[15] 1 1 0.203 1 0.342 0.028
logAlpha_re[16] 1 1 0.187 0 -0.061 0.026
logAlpha_re[17] 1 1 0.467 1 0.939 0.033
logAlpha_re[18] 1 1 0.858 1 0.483 0.032
logAlpha_re[19] 1 1 0.852 0 0.170 0.026
logAlpha_re[20] 1 1 0.390 1 -0.335 0.028
logAlpha_re[21] 1 1 0.726 1 0.792 0.032
logAlpha_re[22] 1 1 0.096 1 -0.666 0.032
logAlpha_re[23] 1 1 0.516 0 -0.165 0.026
logAlpha_re[24] 1 1 0.954 0 -0.039 0.025
logAlpha_re[25] 1 1 0.598 0 -0.027 0.026
tauobs[1] 1 1 0.957 1 0.994 0.010
tauobs[2] 1 1 0.845 1 3.324 0.032
tauobs[3] 1 1 0.216 1 3.302 0.030
tauobs[4] 1 1 0.403 1 4.353 0.039
tauobs[5] 1 1 0.389 1 2.538 0.023
tauobs[6] 1 1 0.335 1 4.033 0.036
tauobs[7] 1 251 0.249 1 1.721 0.015
tauobs[8] 1 1 0.830 1 3.127 0.034
tauobs[9] 1 1 0.875 1 4.155 0.038
tauobs[10] 1 251 0.065 1 2.383 0.021
tauobs[11] 1 1 0.724 1 1.772 0.018
tauobs[12] 1 1 0.102 1 5.338 0.045
tauobs[13] 1 1 0.797 1 5.424 0.042
tauobs[14] 1 1 0.973 1 2.660 0.020
tauobs[15] 1 1 0.281 1 6.486 0.063
tauobs[16] 1 1 0.323 1 4.568 0.047
tauobs[17] 1 1 0.172 1 6.783 0.052
tauobs[18] 1 1 0.953 1 2.192 0.042
tauobs[19] 0 NA 0.007 NA NA NA
tauobs[20] 1 1 0.603 1 2.136 0.019
tauobs[21] 1 1 0.588 1 2.750 0.026
tauobs[22] 1 501 0.276 1 3.109 0.033
tauobs[23] 1 1 0.103 1 2.054 0.015
tauobs[24] 1 1 0.826 1 1.385 0.015
tauobs[25] 1 1 0.421 1 1.454 0.019
logSREP_sd 1 1 0.827 1 0.413 0.007
logAlpha_sd 1 1 0.510 1 0.205 0.007
logAlpha02 1 1 0.334 1 0.291 0.008
lp__ 1 1 0.910 1 -774.671 0.675
Show Chain 4
stest start pvalue htest mean halfwidth
b0[1] 1 1 0.557 1 8.956 0.012
b0[2] 1 1 0.821 1 1.048 0.015
bWA[1] 1 1 0.634 1 0.679 0.004
bWA[2] 1 1 0.569 1 0.284 0.011
logSREP_re[1] 1 1 0.494 1 0.730 0.044
logSREP_re[2] 1 1 0.190 0 -0.077 0.032
logSREP_re[3] 1 1 0.532 1 1.097 0.034
logSREP_re[4] 1 751 0.207 1 -1.041 0.039
logSREP_re[5] 1 1 0.173 1 -0.790 0.031
logSREP_re[6] 1 1 0.880 1 0.381 0.037
logSREP_re[7] 1 1 0.487 0 0.134 0.037
logSREP_re[8] 1 1 0.766 1 -1.031 0.048
logSREP_re[9] 1 1 0.513 1 0.697 0.039
logSREP_re[10] 1 1 0.961 1 0.408 0.028
logSREP_re[11] 1 1 0.841 0 -0.353 0.043
logSREP_re[12] 1 1 0.677 1 0.732 0.033
logSREP_re[13] 1 1 0.378 1 -0.526 0.030
logSREP_re[14] 1 1 0.838 1 0.901 0.030
logSREP_re[15] 1 1 0.845 0 0.267 0.034
logSREP_re[16] 1 1 0.814 1 1.595 0.026
logSREP_re[17] 1 1 0.657 0 0.039 0.046
logSREP_re[18] 1 1 0.478 1 -0.715 0.032
logSREP_re[19] 1 1 0.779 1 -0.539 0.035
logSREP_re[20] 1 501 0.082 1 -0.789 0.044
logSREP_re[21] 1 1 0.841 1 0.787 0.034
logSREP_re[22] 1 1 0.487 1 -1.306 0.034
logSREP_re[23] 1 1 0.924 0 0.319 0.038
logSREP_re[24] 1 1 0.982 1 -0.392 0.034
logSREP_re[25] 1 1 0.750 1 -0.598 0.030
logAlpha0 1 1 0.172 1 1.556 0.007
logAlpha_re[1] 1 1 0.694 0 -0.313 0.034
logAlpha_re[2] 1 1 0.342 1 -0.729 0.037
logAlpha_re[3] 1 1 0.318 0 -0.196 0.033
logAlpha_re[4] 1 1 0.868 1 -0.371 0.036
logAlpha_re[5] 1 1 0.579 0 0.295 0.036
logAlpha_re[6] 1 1 0.630 1 -0.515 0.034
logAlpha_re[7] 1 1 0.644 0 -0.243 0.035
logAlpha_re[8] 1 1 0.712 0 -0.092 0.041
logAlpha_re[9] 1 1 0.462 1 0.924 0.037
logAlpha_re[10] 1 1 0.217 1 -0.613 0.038
logAlpha_re[11] 1 1 0.728 0 0.384 0.045
logAlpha_re[12] 1 1 0.080 1 0.566 0.032
logAlpha_re[13] 1 1 0.463 0 -0.011 0.033
logAlpha_re[14] 1 1 0.345 1 0.491 0.035
logAlpha_re[15] 1 1 0.105 0 0.355 0.038
logAlpha_re[16] 1 1 0.145 0 -0.069 0.030
logAlpha_re[17] 1 1 0.812 1 0.930 0.038
logAlpha_re[18] 1 1 0.411 1 0.472 0.040
logAlpha_re[19] 1 1 0.074 0 0.197 0.036
logAlpha_re[20] 1 1 0.109 0 -0.334 0.040
logAlpha_re[21] 1 1 0.719 1 0.788 0.038
logAlpha_re[22] 1 1 0.777 1 -0.702 0.038
logAlpha_re[23] 1 1 0.336 0 -0.151 0.036
logAlpha_re[24] 1 1 0.685 0 -0.029 0.036
logAlpha_re[25] 1 1 0.740 0 -0.020 0.036
tauobs[1] 1 1 0.844 1 1.002 0.014
tauobs[2] 1 1 0.579 1 3.321 0.037
tauobs[3] 1 1 0.702 1 3.305 0.039
tauobs[4] 1 1 0.531 1 4.364 0.049
tauobs[5] 1 1 0.082 1 2.569 0.031
tauobs[6] 1 1 0.495 1 4.033 0.049
tauobs[7] 1 1 0.784 1 1.725 0.021
tauobs[8] 1 1 0.909 1 3.040 0.043
tauobs[9] 1 1 0.725 1 4.163 0.043
tauobs[10] 1 1 0.758 1 2.375 0.022
tauobs[11] 1 1 0.388 1 1.768 0.022
tauobs[12] 1 1 0.737 1 5.341 0.058
tauobs[13] 1 1 0.817 1 5.397 0.059
tauobs[14] 1 1 0.866 1 2.648 0.029
tauobs[15] 1 1 0.647 1 6.407 0.083
tauobs[16] 1 1 0.773 1 4.524 0.065
tauobs[17] 1 1 0.569 1 6.694 0.069
tauobs[18] 1 1 0.647 1 2.150 0.053
tauobs[19] 1 1 0.552 1 1.749 0.033
tauobs[20] 1 1001 0.054 1 2.107 0.032
tauobs[21] 1 1 0.701 1 2.734 0.037
tauobs[22] 1 1 0.338 1 3.073 0.042
tauobs[23] 1 1 0.441 1 2.050 0.021
tauobs[24] 1 1 0.931 1 1.398 0.021
tauobs[25] 1 1 0.206 1 1.458 0.024
logSREP_sd 1 1 0.674 1 0.406 0.007
logAlpha_sd 1 1 0.192 1 0.209 0.007
logAlpha02 1 1 0.597 1 0.291 0.011
lp__ 1 1 0.711 1 -775.272 0.649

Effective Sample Size

Show table
Parameter EffectiveSize
b0[1] 2597.1
b0[2] 3107.5
bWA[1] 3646.1
bWA[2] 4274.1
logSREP_re[1] 5841.1
logSREP_re[2] 4046.5
logSREP_re[3] 4606.6
logSREP_re[4] 4578.9
logSREP_re[5] 5465.3
logSREP_re[6] 3613.4
logSREP_re[7] 3906.9
logSREP_re[8] 8284.0
logSREP_re[9] 4013.4
logSREP_re[10] 6704.3
logSREP_re[11] 6140.6
logSREP_re[12] 5289.2
logSREP_re[13] 5343.3
logSREP_re[14] 4455.1
logSREP_re[15] 3346.5
logSREP_re[16] 4431.9
logSREP_re[17] 3938.6
logSREP_re[18] 6651.0
logSREP_re[19] 7425.7
logSREP_re[20] 9238.4
logSREP_re[21] 7281.3
logSREP_re[22] 6692.6
logSREP_re[23] 10771.4
logSREP_re[24] 8050.0
logSREP_re[25] 8184.4
logAlpha0 4701.1
logAlpha_re[1] 15022.2
logAlpha_re[2] 10156.7
logAlpha_re[3] 13114.8
logAlpha_re[4] 12007.7
logAlpha_re[5] 11322.7
logAlpha_re[6] 11220.6
logAlpha_re[7] 12325.0
logAlpha_re[8] 8358.0
logAlpha_re[9] 8535.2
logAlpha_re[10] 9648.9
logAlpha_re[11] 12098.3
logAlpha_re[12] 10076.9
logAlpha_re[13] 11395.0
logAlpha_re[14] 12722.8
logAlpha_re[15] 13159.5
logAlpha_re[16] 14233.1
logAlpha_re[17] 8131.8
logAlpha_re[18] 11305.8
logAlpha_re[19] 13282.9
logAlpha_re[20] 10188.9
logAlpha_re[21] 9335.9
logAlpha_re[22] 10219.0
logAlpha_re[23] 10970.9
logAlpha_re[24] 15444.5
logAlpha_re[25] 15986.5
tauobs[1] 17575.5
tauobs[2] 13912.5
tauobs[3] 16397.0
tauobs[4] 15259.9
tauobs[5] 13875.1
tauobs[6] 15905.8
tauobs[7] 15872.5
tauobs[8] 11998.5
tauobs[9] 13559.6
tauobs[10] 16464.7
tauobs[11] 14120.5
tauobs[12] 15229.9
tauobs[13] 15306.8
tauobs[14] 15489.2
tauobs[15] 15856.1
tauobs[16] 16601.8
tauobs[17] 13658.5
tauobs[18] 9992.6
tauobs[19] 14112.2
tauobs[20] 14742.4
tauobs[21] 14751.4
tauobs[22] 14587.1
tauobs[23] 16304.2
tauobs[24] 14263.8
tauobs[25] 14523.4
logSREP_sd 3112.5
logAlpha_sd 2562.9
logAlpha02 4734.1
lp__ 2428.7

Gelman Statistic

Show table
Parameter Point est. Upper C.I.
b0[1] 1.001 1.004
b0[2] 1.000 1.000
bWA[1] 1.001 1.002
bWA[2] 1.000 1.001
logSREP_re[1] 1.000 1.000
logSREP_re[2] 1.001 1.002
logSREP_re[3] 1.000 1.001
logSREP_re[4] 1.001 1.003
logSREP_re[5] 1.001 1.003
logSREP_re[6] 1.000 1.001
logSREP_re[7] 1.001 1.002
logSREP_re[8] 1.000 1.001
logSREP_re[9] 1.001 1.002
logSREP_re[10] 1.000 1.001
logSREP_re[11] 1.000 1.000
logSREP_re[12] 1.000 1.001
logSREP_re[13] 1.002 1.006
logSREP_re[14] 1.000 1.001
logSREP_re[15] 1.001 1.002
logSREP_re[16] 1.000 1.000
logSREP_re[17] 1.000 1.001
logSREP_re[18] 1.001 1.001
logSREP_re[19] 1.000 1.000
logSREP_re[20] 1.001 1.001
logSREP_re[21] 1.000 1.001
logSREP_re[22] 1.001 1.002
logSREP_re[23] 1.001 1.001
logSREP_re[24] 1.000 1.001
logSREP_re[25] 1.001 1.004
logAlpha0 1.000 1.001
logAlpha_re[1] 1.000 1.000
logAlpha_re[2] 1.000 1.000
logAlpha_re[3] 1.000 1.000
logAlpha_re[4] 1.000 1.000
logAlpha_re[5] 1.000 1.000
logAlpha_re[6] 1.000 1.001
logAlpha_re[7] 1.001 1.002
logAlpha_re[8] 1.000 1.001
logAlpha_re[9] 1.000 1.000
logAlpha_re[10] 1.000 1.001
logAlpha_re[11] 1.000 1.001
logAlpha_re[12] 1.000 1.001
logAlpha_re[13] 1.000 1.001
logAlpha_re[14] 1.001 1.001
logAlpha_re[15] 1.000 1.000
logAlpha_re[16] 1.000 1.001
logAlpha_re[17] 1.000 1.000
logAlpha_re[18] 1.001 1.002
logAlpha_re[19] 1.000 1.001
logAlpha_re[20] 1.001 1.002
logAlpha_re[21] 1.000 1.000
logAlpha_re[22] 1.001 1.003
logAlpha_re[23] 1.000 1.000
logAlpha_re[24] 1.000 1.000
logAlpha_re[25] 1.000 1.000
tauobs[1] 1.000 1.001
tauobs[2] 1.000 1.000
tauobs[3] 1.000 1.000
tauobs[4] 1.001 1.001
tauobs[5] 1.000 1.001
tauobs[6] 1.000 1.000
tauobs[7] 1.001 1.001
tauobs[8] 1.001 1.003
tauobs[9] 1.000 1.000
tauobs[10] 1.000 1.000
tauobs[11] 1.001 1.002
tauobs[12] 1.000 1.000
tauobs[13] 1.000 1.001
tauobs[14] 1.000 1.000
tauobs[15] 1.000 1.000
tauobs[16] 1.000 1.001
tauobs[17] 1.000 1.001
tauobs[18] 1.000 1.001
tauobs[19] 1.000 1.000
tauobs[20] 1.000 1.000
tauobs[21] 1.000 1.001
tauobs[22] 1.000 1.000
tauobs[23] 1.000 1.000
tauobs[24] 1.001 1.001
tauobs[25] 1.000 1.001
logSREP_sd 1.003 1.007
logAlpha_sd 1.001 1.002
logAlpha02 1.000 1.000
lp__ 1.001 1.004

5. Prior Predictive Plots

Show figure

6. SR Curves

Show figure: Spawner-Recruit Curves

7. Posterior Residual Plots

Posterior P-Values of logRS Residuals

Show figure: Posterior P-Value for logRS

Where the posterior p-value represents the proportion of simulated means above the observed mean. In this case a value of 0.5414, which indicates a slightly higher bias of the simulated responses over the observations.

Posterior Distribution of logSREP residuals against WA and latitude

Show figure: Residuals of logSREP_re: Ocean Type
Show figure: Residuals of logSREP_re: Stream Type

Residuals of Posterior Predictive against Years and Observed Spawners

Show figure: Residuals of logRS by Year
Show figure: Residuals of logRS by Spawners

Q-Q Norm Plot of Residuals

Show figure: QQNorm Plot of logRS

8. Residual Autocorrelation Plots

Show figure: Residuals ACF of Spawner-Recruit Relationship